Right Bol Loop 16.9.4.4 of order 16


0123456789101112131415
1013121191015142346578
2914151011013121437865
3101514901112134128756
4111213010914153215687
5131101214159108764132
6120111315141097851423
7141091512131106582314
8159101413120115673241
9241378650111014151213
1031428756110915141312
1143216587109013121514
1268751423141513011910
1357864132151412110109
1476583214121315910011
1585672341131214109110

Centre:   0   11

Centrum:   0   11   14   15

Nucleus:   0   11

Left Nucleus:   0   11   14   15

Middle Nucleus:   0   11

Right Nucleus:   0   11


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

9 Elements of order 2:   1   4   9   10   11   12   13   14   15

6 Elements of order 4:   2   3   5   6   7   8

Commutator Subloop:   0   11   14   15

Associator Subloop:   0   11   14   15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,5)(3,6)(7,8)(9,13)(10,12)(14,15) is not an automorphism.   L1,1(2*2) neq L1,1(2)*L1,1(2)

Ar Property:   FAILS. The right inner mapping R1,2 = (1,8)(2,6)(3,5)(4,7)(9,10)(12,13) is not an automorphism.   R1,2(1*1) neq R1,2(1)*R1,2(1)

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001